The present invention relates to an optical member for photolithography, employed as an optical device such as a lens, prism, mirror, correction plate, or photomask for light in a specific wavelength region at 250 nm or shorter, preferably 200 nm or shorter, in the UV lithography technology in particular; and a method of evaluating the same.
In photolithography exposure apparatus for making semiconductor devices such as LSI, liquid crystal display devices, thin-film magnetic heads, or the like, a pattern on a projection original such as a mask or reticle is irradiated with light from a light source by way of an illumination optical system, and the pattern is projected by way of a projection optical system onto a photosensitive substrate such as a wafer or glass plate coated with photoresist beforehand, so as to carry out exposure. Types of the projection optical system include refraction type projection optical systems constituted by lenses adapted to transmit/refract light at an exposure wavelength, reflection type projection optical systems constituted by mirrors adapted to reflect light at the exposure wavelength, and catadioptric projection optical systems combining lenses and mirrors.
In recent years, as the degree of integration has been advancing in semiconductor devices and the like, patterns transferred onto a substrate have been becoming finer. Therefore, photolithography exposure apparatus have been shifting their light sources from i-line (365 nm) to KrF excimer laser (248 nm) and ArF excimer laser (193 nm), and further to F2 laser (157 nm), thus attaining shorter wavelengths. As a consequence, higher optical performances have been required for optical systems for the photolithography exposure apparatus. In particular, projection optical systems for transferring fine mask patterns onto photosensitive surfaces of wafers have been demanded to exhibit quite high optical performances with a high resolution and nearly zero aberrations. For satisfying such a demand, a very high level has been required for the refractive index homogeneity of optical members such as lenses, prisms, mirrors, and photomasks used as optical systems in photolithography exposure apparatus (hereinafter referred to as optical members for photolithography).
Meanwhile, it is important that optical members for photolithography exhibit no unevenness in their refractive index (i.e., have refractive index homogeneity). Conventionally, the refractive index homogeneity of an optical member for photolithography has been evaluated by measuring the wavefront aberration occurring when light passes through the optical member, and using the difference between the maximum and minimum values (here in after referred to as PV value), root mean square (hereinafter referred to as RMS value), or the like of the wavefront aberration as an evaluation index. Specifically, optical members have been thought superior as their PV and RMS values are smaller. Namely, in order to lower these values, optical members considered to be of high quality have been made.
Japanese Patent Application Laid-Open No. HEI 8-5505 discloses a conventional refractive index homogeneity evaluating method. A specific procedure of this method will be explained with reference to FIG. 1.
(1) An optical member for photolithography ground into a columnar or prismatic (rectangular parallelepiped) shape is set to an interferometer, and a reference wavefront is perpendicularly emitted to thus ground surface, so as to measure wavefront aberration (S101). Information resulting from the refractive index distribution of the optical member appears in thus measured wavefront aberration (S102, d101). In this information, an aberration error resulting from a curvature component is referred to as a power element or focus element, whereas that resulting from a tilt component is referred to as a tilt element.
(2) The power and tilt elements are eliminated from the measured wavefront aberration (S103, d102).
(3) Further, the wavefront aberration resulting from the astigmatic element is eliminated (S104, d103).
(4) The remaining wavefront aberration is separated into a rotationally symmetric element and a non-rotationally symmetric (random) element (S105).
(5) The PV and RMS values of the non-rotationally symmetric (random) element are determined, and evaluation is carried out according to these values (d104).
(6) By a least-squares method, the rotationally symmetric element is fitted to an aspheric surface expression (S106), second- and fourth-order components are eliminated therefrom (S107), PV and RMS values of the remaining wavefront aberration components of sixth or higher even order (hereinafter referred to as second- and fourth-order residuals) are determined, and evaluation is carried out according to these values (d105).
As can be seen from the foregoing procedure, optical members having smaller non-rotationally symmetric (random) element and second- and fourth-order residuals have been considered optical members with a favorable refractive index homogeneity, and efforts have been made in order to make such optical members. Namely, optical members have been made heretofore so as to suppress the non-rotationally symmetric element and second- and fourth-order residuals to low levels.
However, optical systems constituted by optical members made so as to exhibit the same RMS and PV values of non-rotationally symmetric element and second- and fourth-order residuals have often yielded imaging performances different from each other. Also, there have been cases where a desirable imaging performance cannot be achieved even when using optical members which have been considered favorable according to the evaluation based on the above-mentioned RMS and PV values. It is needless to mention that semiconductor devices and the like with a high degree of integration are hard to make when using such an optical system failing to achieve a desirable imaging performance. In particular, large-size photolithography optical members exceeding a diameter of 250 mm and a thickness of 40 mm have been problematic in that the disadvantages mentioned above occur frequently when evaluated by the conventional method.
The inventors have found that, by applying a fitting method based on a Zernike cylindrical function system to the evaluation of refractive index homogeneity of individual optical members, the refractive index homogeneity of each optical member can be evaluated more accurately, whereby an optical system achieving a higher-level imaging performance can be constructed more reliably as compared with the case using a conventional refractive index homogeneity evaluating method. Namely, according to the present invention, a photolithography optical member having a high refractive index homogeneity and high quality can be provided more reliably, and not only a high-precision photolithography optical system but also a high-performance photolithography exposure apparatus can be made reliably with a high efficiency.
The present invention provides a method of evaluating a refractive index homogeneity of an optical member for photolithography, the method comprising:
a measurement step of transmitting light having a predetermined wavelength xcex through the optical member so as to measure a wavefront aberration;
a Zernike fitting step of expanding thus measured wavefront aberration into a polynomial of a Zernike cylindrical function system;
a first separating step of separating individual components of the polynomial into a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element; and
a second separating step of separating individual components of the polynomial into a plurality of parts according to a degree thereof.
In the evaluating method of the present invention, the step (first separating step) of separating individual components of the polynomial into the rotationally symmetric element, odd-symmetric element, and even-symmetric element, and the step (second separating step) of separating individual components of the polynomial into a plurality of parts according to the degree thereof may be carried out in any order.
Preferably, in the second separating step, individual components of the polynomial are separated into three parts of lower, middle, and higher orders according to the degree thereof. More preferably, the three parts of lower, middle, and higher orders are terms where n=4 to 8, n=9 to 35, and n greater than 35 in the Zernike cylindrical function system, respectively, whereas a term where n=0 to 3 may be unused for evaluation.
Preferably, in the first and second separating steps is in accordance with the present invention, individual components of the polynomial are classified such that a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=4 to 8 become a lower-order rotationally symmetric element, a lower-order odd-symmetric element, and a lower-order even-symmetric element, respectively; a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=9 to 35 become a middle-order rotationally symmetric element, a middle-order odd-symmetric element, and a middle-order even-symmetric element, respectively; and a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=36 to 80 become a higher-order rotationally symmetric element, a higher-order odd-symmetric element, and a higher-order even-symmetric element, respectively; and a term where n greater than 80 becomes a residual in the polynomial; and
the evaluating method in accordance with the present invention in this case preferably further comprises:
an RMS value calculating step of calculating an RMS value of each of the lower-order rotationally symmetric element, lower-order odd-symmetric element, lower-order even-symmetric element, middle-order rotationally symmetric element, middle-order odd-symmetric element, middle-order even-symmetric element, higher-order rotationally symmetric element, higher-order odd-symmetric element, higher-order even-symmetric element, and residual; and
an evaluating step of evaluating whether thus calculated RMS value satisfies a predetermined condition or not.
The evaluating step preferably evaluates whether at least one of the following conditions (a1), (b1), (c1), and (d1) is satisfied or not:
(a1) each of the respective RMS values of the lower-order rotationally symmetric element, lower-order odd-symmetric element, and lower-order even-symmetric element is 0.06xcex or less;
(b1) each of the respective RMS values of the middle-order rotationally symmetric element, middle-order odd-symmetric element, and middle-order even-symmetric element is 0.02xcex or less;
(c1) each of the respective RMS values of the higher-order rotationally symmetric element, higher-order odd-symmetric element, and higher-order even-symmetric element is 0.005xcex or less; and
(d1) the RMS value of the residual is 0.006xcex or less; and particularly preferably evaluates whether all of the above-mentioned conditions (a1), (b1), (c1), and (d1) are satisfied or not.
Further, the evaluating step preferably evaluates whether at least one of the following conditions (a2), (b2), (c2), and (d2) is satisfied or not:
(a2) each of the respective RMS values of the lower-order rotationally symmetric element, lower-order odd-symmetric element, and lower-order even-symmetric element is 0.02xcex or less;
(b2) each of the respective RMS values of the middle-order rotationally symmetric element, middle-order odd-symmetric element, and middle-order even-symmetric element is 0.008xcex or less;
(c2) each of the respective RMS values of the higher-order rotationally symmetric element, higher-order odd-symmetric element, and higher-order even-symmetric element is 0.003xcex or less; and
(d2) the RMS value of the residual is 0.004xcex or less; and particularly preferably evaluates whether all of the above-mentioned conditions (a2), (b2), (c2), and (d2) are satisfied or not.
It is also preferred that, in the first and second separating steps in accordance with the present invention, individual components of the polynomial be classified such that a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=4 to 8 become a lower-order rotationally symmetric element, a lower-order odd-symmetric element, and a lower-order even-symmetric element, respectively; a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=9 to 35 become a middle-order rotationally symmetric element, a middle-order odd-symmetric element, and a middle-order even-symmetric element, respectively; and a term where n greater than 35 becomes a higher-order residual in the polynomial; and
the evaluating method in accordance with the present invention in this case preferably further comprises:
an RMS value calculating step of calculating an RMS value of each of the lower-order rotationally symmetric element, lower-order odd-symmetric element, lower-order even-symmetric element, middle-order rotationally symmetric element, middle-order odd-symmetric element, middle-order even-symmetric element, and higher-order residual; and
an evaluating step of evaluating whether thus calculated RMS value satisfies a predetermined condition or not.
The evaluating step preferably evaluates whether at least one of the following conditions (a3), (b3), and (c3) is satisfied or not:
(a3) each of the respective RMS values of the lower-order rotationally symmetric element, lower-order odd-symmetric element, and lower-order even-symmetric element is 0.06xcex or less;
(b3) each of the respective RMS values of the middle-order rotationally symmetric element, middle-order odd-symmetric element, and middle-order even-symmetric element is 0.02xcex or less; and
(c3) the RMS value of the higher-order residual is 0.01xcex or less; and particularly preferably evaluates whether all of the above-mentioned conditions (a3), (b3), and (c3) are satisfied or not.
Further, the evaluating step preferably evaluates whether at least one of the following conditions (a4), (b4), and (c4) is satisfied or not:
(a4) each of the respective RMS values of the lower-order rotationally symmetric element, lower-order odd-symmetric element, and lower-order even-symmetric element is 0.02xcex or less;
(b4) each of the respective RMS values of the middle-order rotationally symmetric element, middle-order odd-symmetric element, and middle-order even-symmetric element is 0.008xcex or less; and
(c4) the RMS value of the higher-order residual is 0.004xcex or less; and particularly preferably evaluates whether all of the above-mentioned conditions (a4), (b4), and (c4) are satisfied or not.
Also, the present invention provides an optical member for photolithography used in a specific wavelength band at a wavelength of 250 nm or shorter;
wherein, while a wavefront aberration measured upon transmitting light having a wavelength xcex through the optical member is expanded into a polynomial of a Zernike cylindrical function system, a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=4 to 8 are defined as a lower-order rotationally symmetric element, a lower-order odd-symmetric element, and a lower-order even-symmetric element, respectively; a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=9 to 35 are defined as a middle-order rotationally symmetric element, a middle-order odd-symmetric element, and a middle-order even-symmetric element, respectively; and a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=35 to 80 are defined as a higher-order rotationally symmetric element, a higher-order odd-symmetric element, and a higher-order even-symmetric element, respectively; and a term where n greater than 80 is defined as a residual; the optical member satisfying at least one of the following conditions (a1), (b1), (c1) and (d1):
(a1) each of the respective RMS values of the lower-order rotationally symmetric element, lower-order odd-symmetric element, and lower-order even-symmetric element is 0.06xcex or less;
(b1) each of the respective RMS values of the middle-order rotationally symmetric element, middle-order odd-symmetric element, and middle-order even-symmetric element is 0.02xcex or less;
(c1) each of the respective RMS values of the higher-order rotationally symmetric element, higher-order odd-symmetric element, and higher-order even-symmetric element is 0.005xcex or less; and
(d1) the RMS value of the residual is 0.006xcex or less; and it is particularly preferable that the optical member satisfy all of the above-mentioned conditions (a1), (b1) (c1), and (d1).
Also, the optical member preferably satisfies at least one of the following conditions (a2), (b2), (c2), and (d2):
(a2) each of the respective RMS values of the lower-order rotationally symmetric element, lower-order odd-symmetric element, and lower-order even-symmetric element is 0.02xcex or less;
(b2) each of the respective RMS values of the middle-order rotationally symmetric element, middle-order odd-symmetric element, and middle-order even-symmetric element is 0.008xcex or less;
(c2) each of the respective RMS values of the higher-order rotationally symmetric element, higher-order odd-symmetric element, and higher-order even-symmetric element is 0.003xcex or less; and
(d2) the RMS value of the residual is 0.004xcex or less; and particularly preferably satisfies all of the above-mentioned conditions (a2), (b2), (c2), and (d2).
Further, the present invention provides an optical member for photolithography used in a specific wavelength band at a wavelength of 250 nm or shorter;
wherein, while a wavefront aberration measured upon transmitting light having a wavelength xcex through the optical member is expanded into a polynomial of a Zernike cylindrical function system, a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=4 to 8 are defined as a lower-order rotationally symmetric element, a lower-order odd-symmetric element, and a lower-order even-symmetric element, respectively; a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element in a term where n=9 to 35 are defined as a middle-order rotationally symmetric element, a middle-order odd-symmetric element, and a middle-order even-symmetric element, respectively; and a term where n greater than 35 is defined as a higher-order residual; the optical member satisfying at least one of the following conditions (a3) (b3), and (c3):
(a3) each of the respective RMS values of the lower-order rotationally symmetric element, lower-order odd-symmetric element, and lower-order even-symmetric element is 0.06xcex or less;
(b3) each of the respective RMS values of the middle-order rotationally symmetric element, middle-order odd-symmetric element, and middle-order even-symmetric element is 0.02xcex or less; and
(c3) the RMS value of the higher-order residual is 0.01xcex or less; and particularly preferably satisfying all of the above-mentioned conditions (a3), (b3), and (c3).
Also, the optical member preferably satisfies at least one of the following conditions (a4), (b4), and (c4):
(a4) each of the respective RMS values of the lower-order rotationally symmetric element, lower-order odd-symmetric element, and lower-order even-symmetric element is 0.02xcex or less;
(b4) each of the respective RMS values of the middle-order rotationally symmetric element, middle-order odd-symmetric element, and middle-order even-symmetric element is 0.008xcex or less; and
(c4) the RMS value of the higher-order residual is 0.004xcex or less; and particularly preferably satisfies all of the above-mentioned conditions (a4), (b4), and (c4).
Also, the present invention provides a projection optical system employed in a photolithography exposure apparatus used in a specific wavelength band at a wavelength of 250 nm or shorter, wherein at least 90% of lenses constituting the projection optical system comprise the optical member in accordance with the present invention.
In the projection optical system of the present invention, it is particularly preferred that, in the above-mentioned lenses, a lens having a luminous flux diameter/effective diameter of xc2xd or less comprise an optical member satisfying all of the above-mentioned conditions (a2), (b2), (c2), and (d2) or an optical member satisfying all of the above-mentioned conditions (a4), (b4), and (c4).
Further, the present invention provides a photolithography exposure apparatus used in a specific wavelength band at a wavelength of 250 nm or shorter, the exposure apparatus comprising the projection optical system of the present invention.